Kinematics, driving question

1. The problem statement, all variables and given/known data
you're driving down the highway late one night at 20ms when a deep steps onto the road 35m infront of you. your reaction time before steeping on the brakes is 0.5s and the max deceleration of ur car is 10m/s^2

what is the max speed you could have and still not hit the deer?

deltaX=35m V=?
a=-10m/s^2 reaction time = 0.5s

2. Relevant equations

Xf= Xi+ViT+1/2aT^2
Vf-Vi=aT
Vf^2=Vi^2+1/2a(deltaX)

3. The attempt at a solution
so this is what i tried

i pluged the numbers into the first equation to get

35=0+ViT+1/2(-10)T^2

and i have 2 missing variables so i tried to get it from the other equation

Vf-Vi=aT
0-Vi=(-10)T then that didnt work so i tried the other equation

Vf^2=Vi^2+1/2a(deltaX)
0=Vi^2+1/2(-10)35
Vi= 13.23m/s

and i know that Vi can't be right because i did the question before it and it had Vi of 20m/s and it was 5m from hitting the deer...i dont know what i did wrong can someone help please?1. The problem statement, all variables and given/known data

1. The problem statement, all variables and given/known data
you're driving down the highway late one night at 20ms when a deep steps onto the road 35m infront of you. your reaction time before steeping on the brakes is 0.5s and the max deceleration of ur car is 10m/s^2

what is the max speed you could have and still not hit the deer?

deltaX=35m V=?
a=-10m/s^2 reaction time = 0.5s

2. Relevant equations

Xf= Xi+ViT+1/2aT^2
Vf-Vi=aT
Vf^2=Vi^2+1/2a(deltaX)

3. The attempt at a solution
so this is what i tried

i pluged the numbers into the first equation to get

35=0+ViT+1/2(-10)T^2

and i have 2 missing variables so i tried to get it from the other equation

Vf-Vi=aT
0-Vi=(-10)T then that didnt work so i tried the other equation

Vf^2=Vi^2+1/2a(deltaX)
0=Vi^2+1/2(-10)35
Vi= 13.23m/s

and i know that Vi can't be right because i did the question before it and it had Vi of 20m/s and it was 5m from hitting the deer...i dont know what i did wrong can someone help please?

In order to JUST miss hitting the deer, it must take all 35 meters to slow to 0 m/s. So you have TWO of the equations you just gave: 35=0+ViT+1/2(-10)T^2 for the 35 m and 0-Vi=(-10)T for the time to slow to 0. Now you have two equations in the two "unknown" numbers Vi and T. 0-Vi= -10T tells you that Vi= 10T. Replace Vi by that in the first equation to get a simple equation for T alone. Once you have found T, put that into Vi= 10T to find Vi.